2,041 research outputs found
Parameter Estimation with Mixed-State Quantum Computation
We present a quantum algorithm to estimate parameters at the quantum
metrology limit using deterministic quantum computation with one bit. When the
interactions occurring in a quantum system are described by a Hamiltonian , we estimate by zooming in on previous estimations and by
implementing an adaptive Bayesian procedure. The final result of the algorithm
is an updated estimation of whose variance has been decreased in
proportion to the time of evolution under H. For the problem of estimating
several parameters, we implement dynamical-decoupling techniques and use the
results of single parameter estimation. The cases of discrete-time evolution
and reference-frame alignment are also discussed within the adaptive approach.Comment: 12 pages. Improved introduction and technical details moved to
Appendi
Quantum Portfolios
Quantum computation holds promise for the solution of many intractable
problems. However, since many quantum algorithms are stochastic in nature they
can only find the solution of hard problems probabilistically. Thus the
efficiency of the algorithms has to be characterized both by the expected time
to completion {\it and} the associated variance. In order to minimize both the
running time and its uncertainty, we show that portfolios of quantum algorithms
analogous to those of finance can outperform single algorithms when applied to
the NP-complete problems such as 3-SAT.Comment: revision includes additional data and corrects minor typo
The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations
In this paper we derived the precise formula in a sine function form of the
norm of the amplitude in the desired state, and by means of he precise formula
we presented the necessary and sufficient phase condition for any quantum
algorithm with arbitrary phase rotations. We also showed that the phase
condition: identical rotation angles, is a sufficient but not a necessary phase
condition.Comment: 16 pages. Modified some English sentences and some proofs. Removed a
table. Corrected the formula for kol on page 10. No figure
Understanding Pound-Drever-Hall locking using voltage controlled radio-frequency oscillators: An undergraduate experiment
We have developed a senior undergraduate experiment that illustrates
frequency stabilization techniques using radio-frequency electronics. The
primary objective is to frequency stabilize a voltage controlled oscillator to
a cavity resonance at 800 MHz using the Pound-Drever-Hall method. This
technique is commonly applied to stabilize lasers at optical frequencies. By
using only radio-frequency equipment it is possible to systematically study
aspects of the technique more thoroughly, inexpensively, and free from eye
hazards. Students also learn about modular radio-frequency electronics and
basic feedback control loops. By varying the temperature of the resonator,
students can determine the thermal expansion coefficients of copper, aluminum,
and super invar.Comment: 9 pages, 10 figure
On the adiabatic condition and the quantum hitting time of Markov chains
We present an adiabatic quantum algorithm for the abstract problem of
searching marked vertices in a graph, or spatial search. Given a random walk
(or Markov chain) on a graph with a set of unknown marked vertices, one can
define a related absorbing walk where outgoing transitions from marked
vertices are replaced by self-loops. We build a Hamiltonian from the
interpolated Markov chain and use it in an adiabatic quantum
algorithm to drive an initial superposition over all vertices to a
superposition over marked vertices. The adiabatic condition implies that for
any reversible Markov chain and any set of marked vertices, the running time of
the adiabatic algorithm is given by the square root of the classical hitting
time. This algorithm therefore demonstrates a novel connection between the
adiabatic condition and the classical notion of hitting time of a random walk.
It also significantly extends the scope of previous quantum algorithms for this
problem, which could only obtain a full quadratic speed-up for state-transitive
reversible Markov chains with a unique marked vertex.Comment: 22 page
Magnetic screening in proximity effect Josephson-junction arrays
The modulation with magnetic field of the sheet inductance measured on
proximity effect Josephson-junction arrays (JJAs) is progressively vanishing on
lowering the temperature, leading to a low temperature field-independent
response. This behaviour is consistent with the decrease of the two-dimensional
penetration length below the lattice parameter. Low temperature data are
quantitatively compared with theoretical predictions based on the XY model in
absence of thermal fluctuations. The results show that the description of a JJA
within the XY model is incomplete and the system is put well beyond the weak
screening limit which is usually assumed in order to invoke the well known
frustrated XY model describing classical Josephson-junction arrays.Comment: 6 pages, 5 figure
Optimal estimation of group transformations using entanglement
We derive the optimal input states and the optimal quantum measurements for
estimating the unitary action of a given symmetry group, showing how the
optimal performance is obtained with a suitable use of entanglement. Optimality
is defined in a Bayesian sense, as minimization of the average value of a given
cost function. We introduce a class of cost functions that generalizes the
Holevo class for phase estimation, and show that for states of the optimal form
all functions in such a class lead to the same optimal measurement. A first
application of the main result is the complete proof of the optimal efficiency
in the transmission of a Cartesian reference frame. As a second application, we
derive the optimal estimation of a completely unknown two-qubit maximally
entangled state, provided that N copies of the state are available. In the
limit of large N, the fidelity of the optimal estimation is shown to be
1-3/(4N).Comment: 11 pages, no figure
Pseudo-random operators of the circular ensembles
We demonstrate quantum algorithms to implement pseudo-random operators that
closely reproduce statistical properties of random matrices from the three
universal classes: unitary, symmetric, and symplectic. Modified versions of the
algorithms are introduced for the less experimentally challenging quantum
cellular automata. For implementing pseudo-random symplectic operators we
provide gate sequences for the unitary part of the time-reversal operator.Comment: 5 pages, 4 figures, to be published PR
The Communication Cost of Simulating Bell Correlations
What classical resources are required to simulate quantum correlations? For
the simplest and most important case of local projective measurements on an
entangled Bell pair state, we show that exact simulation is possible using
local hidden variables augmented by just one bit of classical communication.
Certain quantum teleportation experiments, which teleport a single qubit,
therefore admit a local hidden variables model.Comment: 4 pages, 2 figures; reference adde
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